Question

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the ay in this situation?

Answer 1

According to the question, the apparent value of g should become zero at the equator.

We can write,

For apparent g at the equator to be 0 net force acting on the object must be zero so we have to write

$m{w}^{2}R-mg=0$

Or, $w=\sqrt{\frac{g}{R}}=\sqrt{\frac{9.8}{6400000}}=1.24\times {10}^{-3}$ rad/sec

So the earth should rotate with $1.24\times {10}^{-3}$ rad/sec.

Now,

We know that the length of the day is equal to the time of one rotation.

So,

$T=\frac{2\pi }{w}=\frac{2\pi }{1.24\times {10}^{-3}}=5067.7sec=1.41hr$

Hence the length of the day will be 1.41 hr.